Simplify to Amplify: Achieving Information-Theoretic Bounds with Fewer Steps in Spectral Community Detection
This work addresses the problem of improving computational efficiency and performance in spectral community detection for researchers and practitioners, representing an incremental advancement.
The paper tackled community detection in the stochastic block model by proposing a simplified spectral algorithm that eliminates non-essential steps, achieving error bounds approaching information-theoretic limits with tighter rates than prior methods.
We propose a streamlined spectral algorithm for community detection in the two-community stochastic block model (SBM) under constant edge density assumptions. By reducing algorithmic complexity through the elimination of non-essential preprocessing steps, our method directly leverages the spectral properties of the adjacency matrix. We demonstrate that our algorithm exploits specific characteristics of the second eigenvalue to achieve improved error bounds that approach information-theoretic limits, representing a significant improvement over existing methods. Theoretical analysis establishes that our error rates are tighter than previously reported bounds in the literature. Comprehensive experimental validation confirms our theoretical findings and demonstrates the practical effectiveness of the simplified approach. Our results suggest that algorithmic simplification, rather than increasing complexity, can lead to both computational efficiency and enhanced performance in spectral community detection.